1.. _msd:
2
3Mean Square Displacement
4------------------------
5
6| :ref:`gmx msd <gmx msd>`
7| To determine the self diffusion
8  coefficient :math:`D_A` of
9  particles of type :math:`A`, one can use the Einstein
10  relation :ref:`108 <refAllen87>`:
11
12  .. math:: \lim_{t \rightarrow \infty} \langle
13            \|{\bf r}_i(t) - {\bf r}_i(0)\|^2 \rangle_{i \in A} ~=~ 6 D_A t
14            :label: eqnmsd
15
16| This *mean square displacement* and :math:`D_A` are calculated by the
17  program :ref:`gmx msd <gmx msd>`. Normally
18  an index file containing atom numbers is used and the MSD is averaged
19  over these atoms. For molecules consisting of more than one atom,
20  :math:`{\bf r}_i` can be taken as the center of mass positions of the
21  molecules. In that case, you should use an index file with molecule
22  numbers. The results will be nearly identical to averaging over atoms,
23  however. The :ref:`gmx msd <gmx msd>` program can also be used for
24  calculating diffusion in one or two dimensions. This is useful for
25  studying lateral diffusion on interfaces.
26
27An example of the mean square displacement of SPC water is given in
28:numref:`Fig. %s <fig-msdwater>`.
29
30.. _fig-msdwater:
31
32.. figure:: plots/msdwater.*
33    :width: 8.00000cm
34
35    Mean Square Displacement of SPC-water.
36
37
38